SM. and all.
Hornbeam is a hardwood and is of the same genus as Birch, which we use in plywood. Some people mistake its white and very close grained appearence as being Beech.
It is regarded as quite difficult to work with but historically was used to make the teeth for cogs in Windmills, it also has found uses in cutting boards, soles/frames for old woodwork planes, the action parts like hammers and frames in pianos as well as the soles for clogs among other things.
Its whiteness and hardness would make it useful as a decorative inlay but you would need very good sharp tools to machine it and they will blunt quite quickly. It can be waxed or oiled but if you wanted to stain it it might be better to use an alternative.
It can be turned on a lathe and would make ideal rolling pins, dowels etc.
Hope this helps……………PS Willow can indeed be used for stringers and very good it is too, make sure its fully dried.
Cheers…..RON.